Answer:
20 cm
Step-by-step explanation:
For an equilateral triangle the radius of the inscribed circle is half the radius of the circumscribed circle. The radius of the circumscribed circle is ...
2×10 cm = 20 cm.
__
The center of both circles is the centroid of the triangle, which is 1/3 of the distance from a side to the opposite vertex. That is, the centroid-vertex distance is twice the centroid-side distance. The latter is the radius of the inscribed circle; the former is the radius of the circumscribed circle.
